$\dfrac{ 5h + 4i }{ 5 } = \dfrac{ -5h - 9j }{ 10 }$ Solve for $h$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ 5h + 4i }{ {5} } = \dfrac{ -5h - 9j }{ 10 }$ ${5} \cdot \dfrac{ 5h + 4i }{ {5} } = {5} \cdot \dfrac{ -5h - 9j }{ 10 }$ $5h + 4i = {5} \cdot \dfrac { -5h - 9j }{ 10 }$ Multiply both sides by the right denominator. $5h + 4i = 5 \cdot \dfrac{ -5h - 9j }{ {10} }$ ${10} \cdot \left( 5h + 4i \right) = {10} \cdot 5 \cdot \dfrac{ -5h - 9j }{ {10} }$ ${10} \cdot \left( 5h + 4i \right) = 5 \cdot \left( -5h - 9j \right)$ Distribute both sides ${10} \cdot \left( 5h + 4i \right) = {5} \cdot \left( -5h - 9j \right)$ ${50}h + {40}i = -{25}h - {45}j$ Combine $h$ terms on the left. ${50h} + 40i = -{25h} - 45j$ ${75h} + 40i = -45j$ Move the $i$ term to the right. $75h + {40i} = -45j$ $75h = -45j - {40i}$ Isolate $h$ by dividing both sides by its coefficient. ${75}h = -45j - 40i$ $h = \dfrac{ -45j - 40i }{ {75} }$ All of these terms are divisible by $5$ $h = \dfrac{ -{9}j - {8}i }{ {15} }$